The time precipitation needs to travel through a
catchment to its outlet is an important descriptor of a catchment's
susceptibility to pollutant contamination, nutrient loss, and hydrological
functioning. The fast component of total water flow can be estimated by the
fraction of young water (Fyw), which is the percentage of streamflow younger
than 3 months. Fyw is calculated by comparing the amplitudes of sine
waves fitted to seasonal precipitation and streamflow tracer signals. This
is usually done for the complete tracer time series available, neglecting
annual differences in the amplitudes of longer time series. Considering
inter-annual amplitude differences, we employed a moving time window of
1 year in weekly time steps over a 4.5-year δ18O
tracer time series to calculate 189 Fyw estimates and their uncertainty.
They were then tested against the following null hypotheses: (1) at least
90 % of Fyw results do not deviate more than ±0.04 (4 %) from the
mean of all Fyw results, indicating long-term invariance. Larger deviations
would indicate changes in the relative contribution of different flow paths;
(2) for any 4-week window, Fyw does not change more than ±0.04,
indicating short-term invariance. Larger deviations would indicate a high
sensitivity of Fyw to a 1-week to 4-week shift in the start of a 1-year sampling
campaign; (3) the Fyw results of 1-year sampling campaigns started in a
given calendar month do not change more than ±0.04, indicating
seasonal invariance. In our study, all three null hypotheses were rejected.
Thus, the Fyw results were time-variable, showed variability in the chosen
sampling time, and had no pronounced seasonality. We furthermore found
evidence that the 2015 European heat wave and including two winters into a
1-year sampling campaign increased the uncertainty of Fyw. Based on an
increase in Fyw uncertainty when the mean adjusted R2 was
below 0.2, we recommend further investigations into the dependence of Fyw and
its uncertainty to goodness-of-fit measures. Furthermore, while investigated
individual meteorological factors did not sufficiently explain variations of
Fyw, the runoff coefficient showed a moderate negative correlation of r=-0.50 with Fyw. The results of this study suggest that care must be taken
when comparing Fyw of catchments that were based on different calculation
periods and that the influence of extreme events and snow must be
considered.
Introduction
Precipitation water uses slow and fast flow paths on its way through a
catchment to the outlet where it becomes stream water (Tsuboyama et al., 1994). Slow flow
paths are for example the saturated and unsaturated flow through the soil
matrix (Gannon et al., 2017), while fast flow paths include preferential flow (Wiekenkamp et al., 2016a)
and overland flow (Miyata et al., 2009). The distribution of slow and fast flow paths
varies in time and depends on a catchment's spatiotemporal characteristics
(Harman, 2015; Heidbüchel et al., 2013; Stockinger et al., 2014; Tetzlaff et al., 2009a, b). Knowledge of this distribution
helps in assessing the risk of streamflow contamination with pollutants or
nutrient loss, since nutrients and pollutants are transported through the
soil by hydrological pathways (Bourgault et al., 2017; Gottselig et al., 2014).
The water stable isotopes (δ18O and δ2H) are
widely applied in the study of flow paths and transit times of precipitation
through a catchment (McGuire and McDonnell, 2006). One method that utilizes the water stable isotopes
for investigating fast flow paths is the fraction of young water (Fyw).
Developed by Kirchner (2016a), Fyw estimates the streamflow fraction that is
younger than approximately 3 months since entering the catchment as
meteoric water. It does so by comparing the amplitudes of sine waves fitted
to the seasonally varying isotope tracer signals of precipitation and
streamflow. The seasonally varying isotope signal in precipitation is caused
by different evaporation or condensation temperatures, vapor source areas, and
evaporation amounts of falling rain droplets during warmer and colder
seasons, leading on average to higher δ18O values in summer and
lower values in winter (Dansgaard, 1964). As rainfall passes through a catchment to
reach the outlet, this signal is attenuated and shifted in time, leading to
a much smoother but still seasonally varying isotope signal in streamflow.
The ratio of the fitted streamflow sine wave's amplitude AS divided by
the fitted precipitation sine wave's amplitude AP equals the percentage
of water in streamflow younger than 3 months. Kirchner (2016a, b) showed the
robustness of Fyw against spatial catchment heterogeneities (aggregation
bias error), where previous methods of transit time estimation by sine wave
fitting produced highly uncertain results.
Catchment influences on Fyw were investigated globally by, for example, Jasechko et al. (2016).
They calculated Fyw for 254 catchments and concluded that one-third of
global streamflow consists of water younger than 3 months, with
catchments in steeper terrains having smaller contributions of young water
to their runoff. Wilusz et al. (2017) coupled a rainfall generator with rainfall–runoff
and time-varying transit time models to determine the young water fraction.
They found that an increase in annual rainfall amounts of 1 mm d-1 led to an
increase of 0.03–0.04 in the modeled Fyw (percentage point increase of
3 %–4 %, hereafter written as 0.03–0.04, where the value 1 means
that 100 % of streamflow is younger than 3 months). Similar to this,
von Freyberg et al. (2018) found a positive correlation between Fyw and high-intensity
precipitation events. This dependence of Fyw on precipitation
characteristics could lead to long-term changes in Fyw due to global
warming. Global warming was found to increase precipitation intensity and
the frequency of droughts (Pendergrass and Hartmann, 2014; Trenberth, 2011). For Europe, the chance of
extreme heat waves and thus dry conditions has substantially increased since
2003 (Christidis et al., 2015). Previous studies highlighted that the distribution of fast
and slow flow paths is time-variable (Harman, 2015; Heidbüchel et al., 2013). Since Fyw focuses on
fast flow paths, we expect it to be variable in time as well. However, so far
previous studies focused on comparing Fyw between different catchments to
derive relationships between catchment characteristics and Fyw, but no study
has investigated the temporal variability in Fyw for a given catchment yet.
Besides catchment characteristics, the conditions and conceptualizations of
the Fyw calculation also influenced results in past studies. The effect of
varying sampling frequencies of tracer data was investigated by Stockinger et al. (2016). A
higher sampling frequency led to higher Fyw, highlighting the sensitivity of
Fyw to the temporal resolution of the available tracer data. Lutz et al. (2018)
investigated 24 catchments in Germany and used 10 000 Monte Carlo
simulations with random errors in the isotope data of precipitation and
streamflow to derive the 95 % confidence intervals of Fyw. Their
confidence intervals indicated a robustness of Fyw against random errors in
input data. The study of von Freyberg et al. (2018) focused on three influences on Fyw: (a) spatially interpolating precipitation isotopes, (b) including snowpack, and
(c) weighing streamflow in fitting sine waves. They found that weighing
streamflow led to significant changes in Fyw, while the other factors had a
negligible effect.
The mentioned studies highlight the current research interest in the new
measure of Fyw. For this reason, it is necessary to investigate the
sensitivity of Fyw and its uncertainty to different datasets. This is
especially important for catchment comparison studies where the
conceptualization of calculating Fyw might vary between catchments or
datasets of different catchments may vary in quality. The question to answer
is how much of the difference between individual Fyw estimates stems from
actual, catchment-borne differences in flow path distributions and which
part is merely based on, for example, different data quality or quantity.
The present study aims at answering one aspect of this open research
question by focusing on the time variance in Fyw and its associated
uncertainty. Past studies fitted one sine wave to the complete time series
available, varying from less than a year to several decades (Ogrinc et al., 2008; Song et al., 2017;
von Freyberg et al., 2018). To our knowledge, only the study of Stockinger et al. (2017) calculated Fyw for two
different 1-year periods of a multi-year time series but did not test the
temporal variability in Fyw nor influencing factors on it or its
uncertainty. Thus, the sensitivity of the Fyw method towards the timing and
the length of the available data remains to be tested in detail. The present
study investigated the temporal variability in Fyw when different
calculation periods of a multi-year isotope dataset are used. We used a
1-year time window which was shifted in 7 d steps to calculate 189 Fyw
estimates over a 4.5-year time series of isotope data. The 189 Fyw results
were tested against the following null hypotheses:
Fyw estimates do not change over time (time invariance).
Short-term changes in the start of a tracer sampling campaign do not
influence the Fyw estimate (sampling invariance).
Fyw estimates are similar for calculation years that are centered around a
given calendar month (seasonal invariance).
The three hypotheses were tested against whether Fyw differences exceeded a
threshold value of ±0.04, which is the Fyw uncertainty when fitting a
single sine wave to the 4.5-year time series (uncertainty derived by
Gauss error propagation; see Results). We used hydrometeorological and
isotopic data to investigate possible influences on time-variable Fyw
results and their associated uncertainties and, where applicable, to reduce
uncertainty. In conclusion of this study we recommend a tracer sampling
design that reduces Fyw uncertainty.
Material and methodsStudy site
The Wüstebach headwater catchment (38.5 ha) is located in the Eifel
National Park (Germany; Fig. 1). It is also part of the Eifel/Lower Rhine
Observatory of the Terrestrial Environmental Observatories (TERENO) network
(Bogena et al., 2018). The mean annual precipitation amounts to 1107 mm (1961–1990),
with a mean annual temperature of 7 ∘C (Zacharias et al., 2011). Soil is up to 2 m deep, with an average depth of 1.6 m (Graf et al., 2014). Cambisol and
planosol–cambisol soil types are found on hillslopes, whereas gleysols, histosols, and
planosols are found in the riparian zone. The catchment is mostly covered
with Norway spruce (Picea abies) and Sitka spruce (Picea sitchensis; Etmann, 2009). Eight hectares (∼21 %) of the forest were clear-cut in
August–September 2013 (Wiekenkamp et al., 2016b). A severe heat wave occurred in
Wüstebach during summer 2015 (Duchez et al., 2016).
Map showing the Wüstebach catchment and the used monitoring
stations. OP Station is the open precipitation collection site, while TF
Station is the throughfall station.
Data preparation
We used hourly hydrometric and weekly δ18O isotope data of
precipitation (composite sample) and streamflow (grab sample) from October
2012 to June 2017. We did not use δ2H due to the strong
correlation of δ18O and δ2H (R2=0.97 for throughfall and 0.87 for streamflow) and therefore redundancy of
information. Precipitation depths were measured hourly in 0.1 mm
increments for rainfall and daily in 1 cm increments for snowfall at the
meteorological station Monschau-Kalterherberg of the German Weather Service
(Deutscher Wetterdienst – DWD – station 3339, 535 m a.s.l.), located 9 km northwest
of the catchment. Runoff was measured at the outlet by a v-notch weir for
lower and a Parshall flume for higher runoff depths in 10 min intervals.
We collected throughfall samples for isotopic analysis as the Wüstebach
catchment is forested, and the canopy passage of precipitation influences Fyw
(Stockinger et al., 2017). The samples were collected with six RS200 samplers (UMS GmbH,
Germany) with a distance of 2 m to each other and to trees. The samplers
consisted of a 50 cm long, 20 cm diameter plastic pipe which was buried in
the ground. On top of it a 100 cm long plastic pipe with the same diameter
was installed. An HDPE sample bottle (max. volume of 5000 mL) was placed
inside the buried pipe and connected with plastic tubing to a funnel on top
of the 100 cm long pipe. The funnel had a collecting area of 314 cm2 and was protected by a wire mesh against foliage, and a
table tennis ball in the funnel served as an additional evaporation barrier.
Tests of the system showed the reliability in protecting the collected water
from evaporation and in consequence isotopic fractionation for several weeks
(Stockinger et al., 2015). Two samplers of the same design were placed in a clearing of the
Wüstebach catchment to sample open precipitation, i.e., precipitation
that has not passed through the spruce canopy. Streamflow samples for
isotopic analysis were collected weekly as grab samples in HDPE bottles at
the outlet of the catchment.
Isotopic analysis was carried out using laser-based cavity ring-down
spectrometers (models L2120-i and L2130-i, Picarro Inc., USA). Internal
standards calibrated against VSMOW, Standard Light Antarctic Precipitation
(SLAP2), and Greenland Ice Sheet Precipitation (GISP) were used for
calibration and to ensure long-term stability of analyses (Brand et al., 2014). The
long-term precision of the analytical system was ≤0.1 ‰ for δ18O.
We calculated weekly volume-weighed means of δ18O for
throughfall and open precipitation, which were further weighed according to
the respective land-use percentage of spruce forest (79 %) and clear-cut
(21 %) areas to generate a time series of precipitation δ18O
for the whole catchment. The derived precipitation isotope time series was
then used together with the weekly stream water grab samples to calculate
Fyw. While streamflow never ceased and thus a time series of weekly isotope
values was available for the whole time series, there were weeks of no
precipitation and thus gaps in the time series. Because of this, for a
1-year calculation window, on average 43 precipitation isotope values
compared to 53 streamflow values were available. The total number of isotope
values amounted to 156 for precipitation and 195 for streamflow. We could
not always sample precipitation in weekly intervals, leading to bulk samples
of 2–3 weeks on occasion. In this case, we assigned the measured bulk
isotope value to each week, while the measured bulk precipitation depth was
proportionally assigned to each week according to the distribution of hourly
precipitation measured at the meteorological station Kalterherberg.
For further hydrometeorological and isotopic analyses, several additional
data were collected: we measured air temperature and relative humidity in
10 min intervals at the TERENO meteorological station
Schleiden-Schöneseiffen (Meteomedia station, 572 m a.s.l.), located 3 km
northeast of the catchment. We also calculated the runoff coefficient from
runoff (Q) and open precipitation (P) as Q/P and used it for further
analysis. Isotope data were complemented by δ18O values of
groundwater, sampled in four different locations in weekly intervals since
2009. Groundwater was sampled by pumping first to avoid sampling stagnant
water. Lastly, we calculated the d excess of the precipitation samples using
the slope and intercept of the global meteoric water line (d excess =δ2H-8×δ18O; Craig, 1961; Merlivat and Jouzel, 1979).
Fraction of young water
This study will use “Fyw(all)” to refer to the Fyw calculated by using one
sine wave each for the complete 4.5-year time series of precipitation and
streamflow isotope data and “Fyw(189)” for the 189 individual Fyw results
calculated using a 1-year calculation window which was moved in 7 d
steps. A minimum time-window length of 1 year was chosen to fully capture
the annual isotope signal. Fyw is calculated by fitting sine waves to both
the seasonally varying precipitation and streamflow isotope signals. We used the multiple regression algorithm IRLS (iteratively
reweighted least squares; available in the software R) to minimize the
influence of outliers:
CPt=aPcos2πft+bPsin(2πft)+kP,CSt=aScos2πft+bSsin(2πft)+kS,
with CP(t) and CS(t) being the simulated precipitation and streamflow isotope
values of time t, a, and b regression coefficients, and k and f are the vertical shift
and frequency of the sine wave. The difference of CP(t) and CS(t) to the
measured isotope time series in precipitation and streamflow is minimized to
fit the parameters a, b, and k, while the frequency f of the sine wave is
known due to its annual character (i.e., if CP(t) and CS(t) are calculated
in hourly time steps, then the frequency f is 1/8766; once per 24×365.25 h). Precipitation isotope values were weighed using collected
precipitation volumes, while streamflow was weighed using runoff volumes.
The goodness of fit of the sine waves is expressed as the adjusted
coefficient of determination R2 (Radj2),
which accounts for the number of predictors in the regression model. If not
otherwise stated, we will use the mean of the streamflow and precipitation
Radj2, as both sine waves are needed to estimate the
fraction of young water. After fitting the multiple regression equations,
the amplitudes AP and AS and Fyw can be calculated:
AP=aP2+bP2,AS=aS2+bS2,Fyw=ASAP.
Shifting the calculation window in 7 d steps resulted in a time series of
varying Fyw(189) estimates which cannot be considered to be independent of each
other. This precludes the use of regression analysis to derive predictor
variables (e.g., temperature and relative humidity) for the independent
variable (Fyw(189)). However, we used regression analysis to describe the
average meteorological conditions during each Fyw(189) time window. The thus
derived “predictor” variables may have influenced Fyw(189) and could be
investigated in future studies that use independent Fyw estimates.
Fyw calculation was done in a two-step process, as the initial Fyw(189)
results had large uncertainties that originated from a strong influence of
the 2015 European heat wave (see Results and Supplement). Thus,
in a second step we considered its influence and recalculated results while
omitting precipitation isotope data of summer 2015. This greatly reduced
uncertainty. Apart from the Fyw(189) results we also calculated Fyw(all) for
the whole time series with one sine wave, as was the standard of previous
studies. We compared its peak timing and amplitude to the timing of peaks
and amplitudes of the 189 sine waves.
Hypotheses testing
For clarity we want to highlight that each Fyw(189) result was placed in the
midpoint of the year it represents – that is, a data point located at any
date represents the value for the 6 months before and 6 months after
this date. For example, a Fyw(189) result of 0.2 on 6th August 2013 means
that between 5 February 2013 and 4 February 2014, on average
20 % of runoff consisted of water younger than 3 months. The same
logic applies to Radj2 values, amplitudes, phase shifts,
and hydrometeorological data if not explicitly stated otherwise. The
hydrometeorological data were calculated as mean values for the 189
individual calculation years to facilitate comparison to the Fyw(189)
results that are averages valid for the respective calculation time window.
Prior studies in the Wüstebach catchment identified changes of Fyw
between 0.02 and 0.04 as significant (Stockinger et al., 2016, 2017). Here, we employed
Gauss error propagation on the sine wave fit parameters to carry their
respective standard errors through to the Fyw results. Doing this resulted
in uncertainty estimates for the Fyw(189) as well as for Fyw(all). We used
the latter as the threshold value for testing the null hypothesis. In doing
so, the time-variable Fyw(189) values were tested against the uncertainty of the
complete time series. In our study we found a threshold value of 0.04.
Based on this, three hypotheses were tested according to the following rules
of acceptance.
Fyw estimates do not change over time (time invariance).
This hypothesis is accepted if more than 90 % of Fyw(189) values are
within ±0.04 of the mean value of all Fyw(189) values. We chose a minimum
percentage of 90 % to ensure that the long-term time invariance is
captured. Larger changes of Fyw(189) over time would indicate either flow
path changes or a change in the relative contribution of different flow
paths.
Short-term changes in the start of a tracer sampling campaign do not
influence Fyw estimate (sampling invariance).
This hypothesis is accepted if four consecutive Fyw(189) results (i.e., four
weekly shifts of the 1-year time window) do not differ by more than ±0.04. We thus investigated 186 four-week time windows of the total 189
Fyw(189) estimates. The short time span of 4 weeks ensures that the
influence of possible long-term changes in catchment flow paths are not
captured and that only the influence of the start and end time of sampling 1 year of isotope data is investigated. In case that Fyw(189) shows stronger
variations, the sampling time will likely have influenced Fyw(189) results.
Patterns to help identify such situations beforehand are then searched by
analyzing the time of occurrence of these situations.
Fyw estimates are similar for calculation years that are centered around a
given calendar month (seasonal invariance).
This hypothesis tests if the Fyw(189) results centered around a specific
month do not differ by more than ±0.04 within this month. With this we
test (1) if the starting month of a 1-year sampling campaign can influence
Fyw(189) variability and (2) if a “seasonal pattern” can be detected with,
for example, larger Fyw(189) results during 1-year periods centered around
specific months. To clarify, we did not calculate Fyw on a monthly basis but
simply sorted the Fyw(189) results by the month they were assigned to
(midpoint of the calculation year; see also explanation above). If the
hypothesis is accepted, it would indicate seasonal changes in the Fyw(189) as
a function of the start date of a 1-year sampling campaign. This would
allow the pre-planning of sampling campaigns to establish comparable Fyw
results. However, it is also possible that the hypothesis is accepted if
Fyw(189) is constant for all 189 results, as only the intra-month variance
matters with this hypothesis. Contrary to the acceptance of the hypothesis,
rejecting it for most months would indicate that there are no distinct
seasonal patterns imprinted on Fyw(189).
This study does not claim to have found the final rules for judging
differences in Fyw but presents one possible way of doing this by using the
threshold value of 0.04. An example of a theoretical Fyw time series is
given in Fig. 2. All three hypotheses are accepted in this case: the Fyw
results are (1) time-invariant, as all are within the average Fyw plus or minus its
uncertainty (0.04 in this example), (2) sampling-invariant, as within any
4 weeks the maximum difference of Fyw results is less than 0.04, and (3) seasonally varying, as they show a stable seasonal behavior. Therefore,
these results would represent a runoff with a fraction of young water that
systematically varies with the start of the sampling campaign, from a
catchment with stable environmental conditions and water transport
properties and low sampling uncertainties. Under these conditions, starting
a 1-year sampling campaign in different seasons will lead to different Fyw
results, and one needs to take this into consideration when comparing results
from different time periods. However, deciding to wait up to 4 weeks with
the start of the campaign will have no impact on Fyw, while in the long term
the Fyw can be considered stable.
(a) Example of a theoretical Fyw time series, where despite
the time variance, all three null hypotheses are accepted: (1) more than
90 % of Fyw values lie within ±0.04 of the mean of all values, (2) Fyw does not change more than ±0.04 over the course of 4 weeks,
and (3) Fyw for each month does not change more than ±0.04 within a month (b).
ResultsIsotopic and hydrometric data
Precipitation isotope ratios ranged from -3.04 ‰ to
-17.80 ‰, spanning a range of 14.76 ‰
in δ18O values. In comparison, streamflow values ranged from
-7.78 ‰ to -8.74 ‰, with a range of
0.96 ‰ or only 1/15th of precipitation values. The
volume-weighed groundwater isotope value was -8.43±0.17 ‰. The maximum and minimum air temperatures were
27.0 and -7.4∘C, respectively, with a mean value of 7.6 ∘C. Relative humidity ranged from 96.8 % to 32.3 %, with a mean of
82.2 %. All the sampling years except for the winter season 2013–2014 experienced a
build-up of snowpack with a mean height of 15 cm. The absence of snow in
2013–2014 correlated with on average higher temperatures (3.5 times the
average temperature of the other years) and lower relative humidity (5 %
lower average relative humidity compared to the other years). The
hydrometeorological and isotope data are presented in more detail in Sect. 3.3.
Climatological influence on preliminary dataset analysis
Before presenting final Fyw estimates, we briefly introduce the detection and
subsequent remedy of a climatological influence on the initial results and
uncertainties: the initial Fyw(189) values and their uncertainty increased from
July 2014 to December 2015 (Fig. S1 in the Supplement). The uncertainty
reached peak values of ± 0.43. Concurrent with this, Radj2 values dropped close to 0 while being above 0.2 for most other
results. The low goodness of fit and the consequential large uncertainty
could have been caused by outlier values or extraordinary catchment
conditions in Wüstebach. The hydrometeorological and isotopic data
pointed to an influence of the 2015 European heat wave (see Supplement). The heat wave was detectable in the Wüstebach catchment by
the lowest relative air humidity, second lowest rainfall amounts, lowest
runoff coefficient, high temperatures, and the complete disconnection of
precipitation and streamflow amplitudes (Fig. S2). In
addition, the 2015 European heat wave coincided with the lowest surface
water temperatures of the North Atlantic since 1948 (Duchez et al., 2016), which were
visible by the loss of the seasonal d-excess signal. This created a
situation where several months of precipitation isotope signal did not reach
streamflow in Wüstebach. The Fyw method depends on comparable
signals in precipitation and streamflow. Consequently, this disconnection of
precipitation and streamflow added uncertainty to Fyw estimation. Therefore,
we decided to omit the precipitation isotope values between April and July
2015 (11 out of 156 precipitation isotope data; 7 % of the measurements;
Fig. 3a), resulting in less Fyw(189) uncertainty (average: 0.08; maximum:
0.31). We did not omit streamflow data during the same period, as it
contained Fyw information of the previous 3 months of precipitation, and
streamflow sine wave fitting had no impact on Fyw(189) uncertainty (see
results of Fig. 4b).
Sine waves (red lines) were fitted to (a) throughfall and (b) streamflow stable isotope data (grey line), with maximum and minimum values
at each point in time (black enveloping curve). In comparison a single sine
wave was fitted to the complete dataset for both throughfall and streamflow
(green lines). The omitted precipitation isotope values of the 2015 European
summer heat wave are shown in panel (a) with bold black lines.
(a) Fyw(189) results and their uncertainty (black and grey lines)
plotted against Radj2 for throughfall (TF
R2; solid orange line) and runoff (QR2;
dashed orange line) sine wave fits and their average (mean R2; red line). All values are shown at the midpoint of the respective year
they are valid for. Panel (b) shows throughfall amplitudes (TF amplitude)
versus the Fyw uncertainty. The regression equation is TF amplitude =-0.716ln(Fywuncertainty)-0.9236, with an R2 of 0.79. A
similar comparison between runoff amplitudes and Fyw uncertainty showed no
relationship (R2 of 0.04; not shown). The inset shows the Fyw
uncertainty against mean Radj2 values of streamflow and
precipitation.
Isotopic and hydrometric data
After omitting summer 2015 precipitation data the sine waves for the whole
study period had an Radj2 of 0.09 for precipitation and
0.23 for streamflow (Fig. 3). The precipitation amplitude
AP=0.72 ‰ and the streamflow amplitude AS=0.08 ‰ resulted in a Fyw(all) of 0.12±0.04. Thus,
the threshold value for hypothesis testing was chosen as the absolute value
0.04.
The 189 fitted sine waves had a wide range of Radj2
values: precipitation ranged from -0.02 to 0.63, with a mean of 0.22, and
streamflow ranged from 0.00 to 0.55, with a mean of 0.25. The mean
Radj2 (arithmetic average of precipitation
Radj2 and streamflow Radj2) for
each calculation year ranged from 0.03 to 0.59, with a mean of 0.24. The sine
waves showed strong variations in terms of amplitudes and phase shifts,
leading to distinct deviations from the sine wave fitted to the whole time
series (Fig. 3). Precipitation amplitudes ranged between 0.35 ‰ and
2.60 ‰, with a mean value of 1.26 ‰,
while streamflow amplitudes ranged between 0.03 ‰ and 0.19 ‰,
with a mean value of 0.10 ‰. The mean of all streamflow
amplitudes was closer to the single sine wave amplitude
(0.10 ‰ vs. 0.08 ‰) than those for
precipitation (1.26 ‰ vs. 0.72 ‰). If
we use the average of the Fyw(189), the result would be 0.09 instead of 0.12
of Fyw(all). This is less than the 0.04 difference in Fyw used by this
study. Leaving out the period of low Radj2 values, the
single sine wave and the average of Fyw(189) would both yield approximately
0.07. The overall pattern of the individual peaks was similar to the single
sine wave peaks, except for the period of the 2015 European heat wave, when
between June and October 2015, a distinct double peak in precipitation was
visible. The individual sine waves followed the general pattern of enriched
isotopic values during summer months and depleted values in winter.
The mean Radj2 showed a marked decrease during July
2014 to October 2015, with values falling well below 0.2 (Fig. 4a).
Approximately at the same time, the Fyw(189) varied strongly (mean and
maximum change between consecutive 1-year windows: 0.02 and 0.12) and the
uncertainty was large (mean uncertainty: ±0.11). Contrary to this,
during periods of larger Radj2 the change was more
modest (mean and maximum change between consecutive 1-year windows: 0.01
and 0.05) with lower uncertainty (mean uncertainty: ±0.04). To find
possible modeling influences on the Fyw(189) uncertainty, we first compared
the mean Radj2 with it and found that they were
correlated (Fig. 4b inset; R2=0.65). Following this, we
further investigated relationships between Fyw(189) uncertainty and the
amplitudes, phase shifts, and vertical shifts of the 189 sine waves but only
show results for throughfall amplitudes, as the other parameters had no
correlation (Fig. 4b). The throughfall amplitudes were correlated with
R2=0.79, while contrary to this streamflow amplitudes had
an R2 of 0.04. Thus, the Fyw(189) uncertainty was strongly
controlled by the amplitudes of the precipitation sine waves, while the
streamflow sine waves barely influenced it.
The baseline for Fyw(189) was around 0.05 (Fig. 4). Before the low
Radj2 period, Fyw(189) was around 0.05, increased to
about 0.1 for a short time, and then fell back to 0.05. After the low
Radj2 period, Fyw(189) also fell to about 0.05 before
rising in the end. Thus, during the 4.5 years, Fyw(189) values seldom fell below the
baseline of 0.05, and we assumed that during any 1-year period the
Wüstebach catchment will have at least a 0.05 Fyw. Overall, the Fyw(189) values
were positively skewed (Fig. 5). Around 30 % of results indicated a Fyw
of 0.06, followed by 55 % of results that indicated a Fyw up to 0.08. Few
values are higher than 0.16, with possible outliers between 0.26 and 0.28.
Leaving out the period of low Radj2 values does not
change the skewness of the histogram. However, values larger than 0.16
disappeared in favor of 0.06 that shifted from 30 % to 40 % relative
frequency.
Histograms and cumulative distribution functions of all Fyw(189)
results (black) and of the results when the low Radj2
period is left out (low R2; grey).
Hypothesis 1: time invariance
The mean of Fyw(189) was 0.09. Consequently, 90 % of all Fyw(189) results
must lie within 0.05 to 0.13 to accept hypothesis 1; 159 Fyw results (84 % of
the 189) were within those boundaries (Fig. 6a). It could be possible that
the period between July 2014 and October 2015 with low Radj2 significantly influenced the rejection of the hypothesis.
Therefore, in a second step, we excluded this period, calculated the mean for
those values and evaluated the results again (Fig. 6b). The new mean Fyw
was 0.07, with 93 % of results found between 0.03 and 0.11. Thus, contrary
to using all data, the hypothesis could be accepted if the period of large
uncertainty is left out. We then compared the time-variable Fyw(189) to
hydrometeorological measurements (Fig. 7) and found that neither
temperature nor relative humidity were correlated with it (not shown). While
throughfall volume, runoff volume, and snow height were also not correlated
(Fig. 7a–c), the runoff coefficient (Q/P) was negatively correlated with
R2=0.25 and p=1.7×10-11 (Fig. 7d). Leaving out
again the period from July 2014 to October 2015 reduced the correlation to
R2=0.08 and p=9.8×10-4.
Fyw(189) compared to the mean Fyw (solid grey line) and a ±0.04 margin around it (dotted grey lines) to test hypothesis 1 (90 % of
all Fyw results are within the mean Fyw ±0.04). Red data points are
periods where within 4 weeks, Fyw differed by more than 0.04 (testing
hypothesis 2). Once all data were used (a), subsequently data of the
low Radj2 period between July 2014 and October 2015 were
left out (b).
Fyw(189) plotted against hydrometric data (red and black dots): (a) throughfall volumes, (b) runoff volumes, (c) snow height, and (d) the runoff
coefficient. Red dots are data points where hypothesis 2 was rejected (Fyw
does not differ by more than ±0.04 within 4 consecutive weeks).
Hypothesis 2: sampling invariance
Here we tested if deciding to delay the start of a 1-year sampling
campaign up to 4 weeks could influence Fyw(189). The hypothesis is
accepted if any four consecutive Fyw(189) results did not differ by more than
0.04. On multiple occasions this rule was violated for the full dataset as
well as for the reduced one (discounting the low Radj2
period), so we rejected hypothesis 2 (Fig. 6). Thus, the start time of a
1-year sampling campaign influenced Fyw(189). The periods when
hypothesis 2 was violated were neither equally spaced in time (Fig. 6) nor
showed significant correlations to hydrometric (Fig. 7) or
meteorological (not shown) variables. The only observation made was that
hypothesis 2 seems to have preferentially failed around the 2015 European
heat wave.
Hypothesis 3: seasonal invariance
As mentioned in the methods, the Fyw(189) results were put in the middle of
the 1-year calculation period (calculating from February 2016 to February
2017, the result would be displayed as a data point in August 2016). We
grouped together all Fyw(189) values that were assigned to a specific calendar
month and used a boxplot to detect possible seasonality (Fig. 8). Only in
January and February was the difference below 0.04. When leaving out the
period with low Radj2, January to August stayed within
±0.04. Thus, we also rejected hypothesis 3 based on all data, as our
results did not indicate pronounced seasonality. Nonetheless, a trend of
declining Fyw(189) from January to June was visible that reversed from July
onwards. Additionally, the standard deviation of Fyw(189), the interquartile
range of the boxplots, and the number of outliers increased starting with
June until October–November. We compared this behavior qualitatively to the
start and end time of snow influence in Wüstebach, which usually
started in December, and the last melt event happened in February. Since the
influence of this delayed signal transmission from precipitation to
streamflow does not immediately end with the final snowmelt in February, we
assumed that snowmelt still influenced streamflow for the following 2 months, i.e., until April. This comparison showed that calculation years
that included one year's winter had lower interquartile ranges, a lower
number of outliers, and smaller standard deviations. On the other hand,
calculation years that included winters of two different years (e.g., a
calculation year starting and ending in December) matched the boxplot
results with increased uncertainty (Table 1).
Testing hypothesis 3 (Fyw centered around a specific month does not
differ by more than ±0.04 within this month): boxplot of all Fyw results
of a specific month. Whiskers are the upper and lower 1.5 interquartile
range, and circles are outlier values. The number of data points for each
month is given in the brackets on the horizontal axis.
The calculation years used for the boxplots of Fig. 8.
For example, the first row shows a calculation year starting in July and
ending in July, where the Fyw result was assigned to January. Grey shaded
areas are the usual beginning of snowfall and the final snowmelt (December to
February; dark shading), with an assumed prolonged influence of snowmelt on
streamflow until April (light shading). Green calculation years
highlight snow influence of only one winter within this year, while red
calculation years highlight influence of two different winters.
Discussion
Judging by the isotope data, we generally expect that groundwater was
recharged locally from precipitation, as the long-term, volume-weighed
δ18O of precipitation with -8.53 ‰ was close
to the quasi-constant δ18O of groundwater with a 5-year mean of
-8.43±0.17 ‰. Streamflow was substantially
comprised of groundwater, as its volume-weighed δ18O was
-8.40 ‰, the precipitation isotope signal was strongly
attenuated in streamflow, and Fyw(189) values were generally low, which
indicates a strong groundwater influence. The study by Weigand et al. (2017) came to the
same conclusion for the Wüstebach catchment using wavelet analysis of
nitrate and DOC data collected at mainstream and tributary locations. While
lower-altitude locations of the catchment near the outlet were dominated by
groundwater, higher-altitude areas were less affected. This finding was
additionally supported by field observations of shallow groundwater.
Sine wave fits
The single sine wave fits to all data had low Radj2
values (0.09 for throughfall and 0.23 for streamflow). Compared to this, the
189 individual sine waves reached a maximum Radj2 of
0.63 and were often larger than 0.2. This indicated that the single sine
wave fit to multi-year data is an oversimplification of the inter-annual
variability in meteoric and streamflow isotope data, and annual sine waves
better capture the variability. One might argue that sine waves are a
non-adequate function to describe the data variability if their
Radj2 is low. However, Fyw estimation is based on
comparing sine wave amplitudes (Kirchner, 2016a), and no similar method exists to
calculate it with different functions.
Completely undetectable by a single sine wave fit, the 189 sine waves
highlighted a hydrologic change in the Wüstebach catchment caused by the
2015 European heat wave: the disconnection of precipitation and runoff.
First, the general shapes of the 189 precipitation and 189 streamflow sine
waves were similar (Fig. 3), which can be seen, for example, in the positive and
negative peaks occurring around September 2014 and 2016 and February 2013
and 2014, respectively. Additionally, throughfall and streamflow amplitudes
generally matched each other (Fig. S2a). This indicated that
throughout the 4.5-year time series the characteristic of the precipitation
δ18O signal was for the most part consistently and quickly
transferred to the streamflow δ18O signal within a year.
However, the relationship between precipitation and streamflow considerably
changed due to the influence of the 2015 European heat wave: while the
double peak of the sine fits to the precipitation isotopes in summer 2015
was not transferred to streamflow (Fig. 3), the seasonal cycle amplitudes
of the isotopes in streamflow and precipitation lost their close
relationship at the same time (Fig. S2a). After the heat
wave the general shape of precipitation and streamflow sine waves matched
each other again while their respective amplitudes regained their former, albeit weakened,
relationship: the large amplitude peak in throughfall in
April 2016 again led to increasing streamflow peaks. The 2015 European heat
wave greatly disturbed the usually occurring runoff-generation process in
Wüstebach, leading to a disconnection of precipitation and
streamflow signal.
A fast transmission of precipitation to streamflow was also found by
Jasechko et al. (2016), and the fact that a part of precipitation quickly becomes
streamflow is already inherent in Fyw. The new insight of the present study
is the unexpected close resemblance of the 189 sine waves for precipitation
and streamflow, although the groundwater influence seems to have dominated in
Wüstebach. The simultaneous strong attenuation of the δ18O streamflow signal while at the same time retaining much of the
precipitation δ18O signal characteristics can be explained by
mixing with a quasi-constant δ18O source, e.g., with
groundwater. This would not alter the pattern but only attenuate the signal.
Thus, the 189 sine waves strongly indicated that streamflow in
Wüstebach consisted of precipitation and groundwater with no additional,
unaccounted sources of runoff such as subsurface flows from outside the
catchment boundaries, although additional sources are still theoretically
possible. This supports a previous study that closed the water balance for
the Wüstebach catchment using only precipitation, evapotranspiration, and
runoff data (Graf et al., 2014) and is essential information for, for example,
endmember-mixing analysis (Barthold et al., 2011; Katsuyama et al., 2001) or isotope hydrograph
separation (Klaus and McDonnell, 2013). The 189 sine wave fits to precipitation and streamflow
isotope data facilitated finding this hydrological information about the
Wüstebach catchment.
Fraction of young water
The fact that the average of Fyw(189) was within the ±0.04 boundary
of Fyw(all) (0.09 vs. 0.12) indicated that the single sine wave generally
averaged the behavior of the 189 ones. If the isotope data and Fyw(189)
results of the period of low Radj2 values were left out,
the average Fyw of the 189 sine waves compared even better to Fyw(all)
(approximately 0.07 in both cases). Thus, if a study is interested in the
overall behavior of a multi-year time series, a single sine wave fit would
seem sufficient. Nevertheless, hypothesis 1 was rejected, as Fyw(189) varied
within this multi-year time series (Fig. 6). Using a moving time window to
calculate a host of Fyw values ensures that the entire range of possible Fyw
estimates is considered with an average estimate and most importantly its
uncertainty.
Most of the isotope data between 7 d calculation window shifts were the
same. Still, during the low Radj2 period, Fyw(189)
occasionally fluctuated on the order of 0.12 between 1-week shifts. From a
hydrological standpoint, it is difficult to imagine a short-term change in
flow paths of this magnitude for annual averages. Given that the Fyw
calculation is based on comparing the amplitudes of precipitation and
streamflow and a low Radj2 indicates a weak fit to a
sine wave shape, we assumed that in our case the Fyw calculation method
reached its limit below an average of Radj2=0.2.
Fyw(189) became highly sensitive to a small change in input data and, in
consequence, highly uncertain. We recommend further investigations of the
sensitivity of Fyw to the goodness of fit (not necessarily only measured
with Radj2) for future studies. It remains to be seen
if a value of 0.2 for Radj2 is a general critical
threshold for Fyw or if different catchments show varying results. Such
studies should consider that the Fyw uncertainty was correlated with
throughfall amplitudes (Fig. 4b), raising the question of whether a curve fit with
Radj2=0.6 is objectively better than a fit with
Radj2=0.3 when the underlying isotope data have
completely different amplitudes. A decrease in the goodness of fit of the
sine wave when amplitudes are low was also found by Lutz et al. (2018).
A difference of ±0.04 was defined as the threshold value for
differences in Fyw(189) by this study. The acceptance or rejection of our
null hypotheses will thus inform if the time variability in Fyw(189) is
large in comparison to Fyw(all) and its uncertainty. We recommend using
different thresholds that are suited to the purpose of calculating a Fyw
estimate. Purposes can range from any application of the method to answer
questions about the quantity and quality of water resources for various
industrial, touristic, or infrastructural uses. First, a critical difference
in Fyw should be defined by each application that reflects, for example, the
vulnerability of aquatic ecosystems to certain pollutant loads. If an
increase or decrease by less than this value does not impact the results of
a risk assessment, for example, then these Fyw changes are negligible for the
practical purpose at hand. The present study did not aim to answer any
specific question related to Fyw that would justify setting a threshold
value a priori but investigated the time variability in Fyw and used the
uncertainty as its threshold value. Thus, the results of the hypothesis
tests might change completely if we answer practical questions about
Wüstebach, such as the vulnerability to pollutant loads of a certain
chemical substance. Choosing different rules for the acceptance or rejection
of our hypotheses has a large impact on the results. The hypotheses and
rules of acceptance should be fitted to the task at hand, and we urge further
studies to investigate appropriate rules for the practical usage of Fyw, as
we do not claim to have found the absolute answer in deciding which Fyw
results are different and which are not.
The 2015 European heat wave was among the top 10 heat waves of the past 65
years and was accompanied by the lowest surface water temperatures of the
North Atlantic in the period of 1948 to 2015 (Duchez et al., 2016). The North Atlantic
influences the European summer climate (Ghosh et al., 2017) and is an important vapor
source for precipitation over Europe (Hurrell, 1995; Trigo et al., 2004). The combined effects
of low ocean water temperatures and high air temperatures in Europe were
visible in the d excess that lost its clear seasonal signal in summer 2015
(Fig. S2d). The d excess of precipitation samples is
strongly controlled by the relative humidity of the moisture source (Pfahl and Sodemann, 2014;
Steen-Larsen et al., 2014), which in turn would change with changing surface water temperatures
and thus changing evaporation rates. Additionally, the increased European
air temperatures during the heat wave would increase secondary evaporation
of falling raindrops, further altering the d excess of precipitation
samples. The North Atlantic and European temperature anomalies of 2015
explain the behavior of the d excess as well as the unusual double peak of
the 189 sine waves that was observed for summer 2015 in Wüstebach.
Apart from affecting the isotopic input signal into the Wüstebach
catchment, the temperature anomalies of 2015 also changed the hydrological
behavior of Wüstebach: precipitation was largely disconnected from
streamflow, and the isotopic signal was not transferred (Fig. S2a–c). This directly increased Fyw(189) uncertainty during this period.
Future studies must be careful in comparing Fyw estimates of different time
periods, especially if a heat wave occurred during those periods. We assume
that mostly small headwater catchments with shallow soils are strongly
affected by this effect but do not exclude the possibility of other
catchments being affected in varying degrees too. It is highly advisable to
investigate further in this direction, as the probability of heat waves in
the period from 2021 to 2040 is poised to increase (Russo et al., 2015). This, by
extension, means that the probability of getting highly uncertain Fyw
results will increase too. We argue that heat waves are actively disturbing
the estimation of Fyw by potentially decoupling the input from the output
isotope signal. This can be more clearly illustrated by the theoretical
worst-case scenario: the decoupling of precipitation and streamflow signal
for a full year and streamflow being solely fed by another source, e.g.,
groundwater. Why, in this case, would we trust the Fyw result, no matter the
magnitude of the uncertainty and goodness of fit of the sine wave? Thus, it is
reasonable to assume that any amount of decoupling will add uncertainty to
Fyw, as demonstrated by our data and results. Only by comparison to other
time frames where the uncertainty was smaller was it possible for us to
detect that the uncertainties for summer 2015 were unusually large.
Hypothesis 1 – Fyw is time-variant
Hypothesis 1 was rejected because the Fyw varied in the long term. For
example, in December 2013, Fyw was 0.06, while 2 months later it increased
to 0.1, almost doubling. From summer 2016 to the end of the time series, Fyw
even tripled, from 0.06 to 0.15. These differences in Fyw results complicate
catchment comparisons, as the result does not only depend on catchment
characteristics but also on when isotope data were collected. As far as we
can tell, the recent Fyw catchment comparison study of Lutz et al. (2018) used the
same sampling period for precipitation and streamflow for all 24
investigated catchments. In contrast, the studies of Jasechko et al. (2016) and von Freyberg et al. (2018)
had isotope sampling periods varying in start date and overall length for
the 254 and 22 investigated catchments, respectively, potentially
influencing the uncertainty for the inter-catchment comparison according to
the results of our study.
In the Wüstebach catchment the baseline for Fyw(189) was around 0.05.
This lower boundary is useful in assessing pollutant risk and nutrient loss
in the catchment, as it defines a minimum expected load that will quickly
appear in the stream if combined with precipitation volumes and chemical
substance concentrations. The lower boundary of this study is only valid for
the Wüstebach catchment, as other catchments might have different lower
Fyw boundaries.
The variability in Fyw(189) of this study could not be explained by
meteorological or hydrometric variables. Lutz et al. (2018) found a negative
correlation between annual precipitation and Fyw. The study of 22 Swiss
catchments by von Freyberg et al. (2018) found significant positive correlations between Fyw
and mean monthly discharge and precipitation volumes. Fyw(189) of this study
neither correlated with precipitation nor with runoff (Fig. 7a and b). Such contradictions could be explained by the different sampling
periods of our study and the mentioned studies but also by differing
catchment characteristics. Additionally, the present study investigated the
same catchment temporally, while the other studies investigated spatially
different catchments. Furthermore, Lutz et al. (2018) found complex interactions
between several catchment characteristics and Fyw, possibly resulting in
nonsignificant linear regressions between Fyw and individual catchment
characteristics. However, the runoff coefficient Q/P was negatively
correlated with Fyw(189) (Fig. 7d). Physically, this could be explained by
the fact that if annual runoff volumes increase per annual precipitation
volume, then the additional runoff volumes were provided by catchment
storage. This increased the percentage of old water in streamflow and
relatively decreased the Fyw(189), since catchment storage consists of old
water (Gabrielli et al., 2018).
Hypothesis 2 and 3 – Fyw is sensitive to sampling and has no clear
seasonal pattern
While hypothesis 1 concentrated on long-term changes, hypothesis 2 focused
on short-term changes where choosing to start a 1-year sampling campaign
1 to 4 weeks later could lead to different results. On several
occasions, Fyw(189) differed more than ±0.04 within 4 weeks (Fig. 6). This means that the choice of the sampling period has a large potential
for uncertainty in the Fyw estimates for studies that can monitor the water
stable isotopes in precipitation and streamflow for only 1 year. The
obtained Fyw could be a potential outlier, a larger value, or part of a
theoretical Fyw baseline. As the timing of the violation of hypothesis 2 did
not correlate with any meteorological or hydrometric data, it was not
possible to determine the conditions under which the sampling period led to
higher Fyw(189) uncertainty. A relationship with the 2015 European heat wave
is possible, albeit not fully evident. Nonetheless, as discussed above, the
choice of another threshold value besides ±0.04 may lead to an
increase in the number of short-term Fyw(189) changes. The results of this
study indicate that estimating Fyw with data of a single year might not be
enough for fully understanding catchment behavior. Quoting Kirchner et al. (2004): “If we want to understand the full symphony of catchment
hydrochemical behavior, then we need to be able to hear every note”. A
single Fyw result is one note in the symphony of potential Fyw results
in multi-year datasets.
Fyw(189) did not have a clear seasonal pattern in that not all the months
had differences of less than ±0.04 (Fig. 8). A pattern was
nonetheless visible with larger Fyw(189) values with less uncertainty when the
sampling campaign was centered around winter months compared to lower
Fyw(189) values with larger uncertainties when the campaign was centered around
summer months. Thus, the starting month of a 1-year sampling campaign did
influence Fyw(189) variability, and 1-year periods centered around winter
months led to generally larger values in our study. The behavior of Fyw(189)
uncertainty can potentially be explained by the influence of snow and is
similar to the proposed problem that the 2015 European heat wave introduced:
a tracer signal in precipitation and streamflow that does not have any
instantaneous connection with its counterpart streamflow and precipitation. This
disconnection by snow could be explained by the longer delay in signal
transmission of snowfall compared to rainfall due to snowpack build-up.
Consider a winter at the start of a sampling campaign: it is likely that
streamflow will feature the snowmelt isotope signal originating from
snowfall of, for example, several weeks ago that is not featured in the
precipitation isotope data of this calculation year. Currently, we recommend
that if studies can only sample 1 year of data in snow-influenced
catchments, they should not sample winters of two different calendar years and should
design the sampling such that only one year's winter is in the time series.
Future studies should provide more evidence if Fyw calculated by 1 year of
isotope data shows a seasonal behavior or not and how snow influences the
uncertainty. We highly recommend calculating a time series of Fyw, e.g.,
with the method of this study, to understand the temporal behavior of Fyw
for the investigated catchment and to be able to evaluate possible
uncertainties for Fyw estimation.
A difference in Fyw when only 1 year of isotope data are available was also
observed by Stockinger et al. (2017) for the same catchment using only two calculation years
without any further investigations in this direction, as it was not the main
objective of their study to investigate Fyw time variability and
uncertainty. Only two Fyw values were calculated in contrast to the 189 results of
the present study. This low number of results made it impossible to
investigate possible causes of varying Fyw results and to judge if those
results were the rule or an exception. Fyw values for these years were 0.06 and
0.13, respectively. The authors assumed that using the complete time series
averages sub-sets of the time series as the Fyw for the whole time series
was approximately 0.13, so in between 0.06 and 0.13. However, this happened
by coincidence. The present study shows that the two Fyw values could have been
very different, e.g., both near 0.05. Then, the Fyw of the whole time series
would not have averaged the results of the two individual years. Thus, only
the complete picture of all 189 individual Fyw(189) results allowed a better
judgment of time variability and uncertainty. With knowledge from the
current study, we would even consider one of the hydrological calculation
years of Stockinger et al. (2017) to be highly uncertain and possibly influenced by the 2015
European heat wave.
Conclusions
The fraction of young water (Fyw) is a promising new measure to estimate the
fast transport of precipitation through a catchment to the stream. To
calculate Fyw, sine waves are fitted to the water stable isotopes in
precipitation and streamflow and their respective amplitudes compared. This
is usually done for the complete time series available, ranging from less
than a year to multiple years. This study used a moving 1-year window to
investigate the temporal variance in Fyw and its uncertainty for a 4.5-year
time series. Using 189 Fyw results instead of a single multi-year one,
we were able to increase our hydrometeorological knowledge about the study
catchment: (1) a potential strong influence of the 2015 European heat wave
on Fyw estimates and uncertainties was discovered, which is a problem which
could be magnified in the future when considering global warming, and (2) a lower boundary
for Fyw was found, aiding, for example, pollutant risk studies in calculating minimum
expected loads. Testing three hypotheses about the time variability in
Fyw(189), we found that both in the long term and short term, Fyw(189) was
time-variable as defined by this study by the ±0.04 threshold, while
showing no clear seasonal pattern. The long-term variability has
implications for catchment comparison studies when different time periods
are investigated. Short-term variability indicated a potentially high
sensitivity to the sampling period, where a shift of 1–4 weeks in the start
of a 1-year sampling campaign influenced Fyw. No pronounced
seasonality of Fyw(189) could be derived. However, a possible influence of
snowpack led to the recommendation of sampling one year's winter and
avoiding sampling the winters of two different years. If feasible, we
recommend investigating a multi-year time series of tracer data with the
method suggested in this study to enhance our knowledge of the sensitivity
of Fyw to the chosen time frame in different catchment situations and the
behavior of its uncertainty – that is, to use a 1-year moving time window
and estimate an ensemble of Fyw results and its uncertainty. Based on the
goodness of fit for all 189 calculated sine waves and the corresponding
Fyw(189) behavior, we recommend considering that Fyw based on
Radj2 below 0.2 might be highly uncertain. This must be
verified by other dedicated studies of different catchments and would allow
for a better comparability of Fyw results with various goodness of fits. The
present study shows the importance of considering inter-annual fluctuations
in the amplitudes of isotope tracer data and consequently of derived Fyw
estimates in further learning about the uncertainty of Fyw and in aiding in
catchment comparison studies.
Data availability
The data used in this study can
be acquired from the corresponding author.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-23-4333-2019-supplement.
Author contributions
MPS designed the study and carried out the calculations. HRB, AL, CS, and HV contributed to the interpretation of results, and all authors contributed to the writing of the paper.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
We gratefully acknowledge the support by the SFB-TR32 “Patterns in
Soil-Vegetation-Atmosphere Systems: Monitoring, Modelling, and Data
Assimilation” funded by the Deutsche Forschungsgemeinschaft (DFG) and
TERENO (Terrestrial Environmental Observatories) funded by the
Helmholtz-Gemeinschaft. Holger Wissel, Werner Küpper, Rainer Harms,
Ferdinand Engels, Leander Fürst, Sebastian Linke, and Isabelle Fischer
are thanked for supporting the isotope analysis, sample collection, and the
ongoing maintenance of the experimental setup. We appreciate the helpful
comments of four anonymous reviewers that greatly improved the present
study and the work of editor Patricia Saco. We additionally thank Giuseppe Brunetti for proofreading the paper.
Financial support
This research has been supported by the Deutsche Forschungsgemeinschaft (grant no. SFB TR 32).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.
Review statement
This paper was edited by Patricia Saco and reviewed by four anonymous referees.
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